Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments
Infinite Cardinalities, Measuring Knowledge, and Probabilities in Fine-Tuning Arguments
This chapter deals with two different problems in which infinity plays a central role. It first responds to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and it argues that we should use the subset principle for measuring knowledge. The chapter then turns to the normalizability and coarse tuning objections to fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, the chapter hopes to blunt much of the force of these objections to fine-tuning arguments.
Keywords: fine-tuning arguments, infinity, measuring knowledge, multiverse, existence of God
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